On Catastrophic Forgetting in Low-Rank Decomposition-Based Parameter-Efficient Fine-Tuning

Parameter-efficient continual learning aims to adapt pre-trained models to sequential tasks without forgetting previously acquired knowledge. Most existing approaches treat continual learning as avoiding interference with past updates, rather than considering what properties make the current task-specific update naturally preserve previously acquired knowledge. From a knowledge-decomposition perspective, we observe that low-rank adaptations exhibit highly imbalanced singular value spectra: a few dominant components absorb most of the adaptation energy, thereby (i) more likely to disrupt previously acquired knowledge and (ii) making the update more vulnerable to interference from subsequent tasks. To enable explicit balance among components, we decouple the magnitude of the task update from its directional structure and formulate it as a constrained optimization problem on a restricted Stiefel manifold. We address this problem using a projected first-order method compatible with standard deep-learning optimizers used in vision-language models. Our method mitigates both backward and forward forgetting, consistently outperforming continual learning baselines. The implementation code is available at https://github.com/haodotgu/EBLoRA.

Sequential fine-tuning of pretrained language encoders often overwrites previously acquired capabilities, but the forgetting behavior of parameter-efficient updates remains under-characterized. We present a controlled empirical study of Low-Rank Adaptation (LoRA) in sequential transformer encoder fine-tuning with companion representation probes that test a frozen-backbone explanation of its robustness. In five full-validation BERT-base reruns on an RTE->MRPC->CoLA->SST-2 sequence, full fine-tuning yields 19.9%+/-4.8% average forgetting, whereas standard LoRA (r=8, query/value modules) yields 0.6%+/-1.4% (paired t-test, p=0.002, Cohen's d_s=3.12). Task-level analyses confirm this reduction is not merely an aggregate effect. Secondary experiments on RoBERTa-base show the same pattern, and the strongest EWC baseline remains at 15.5%+/-1.4% forgetting. A six-task extension reveals that low average forgetting can hide strong task-level heterogeneity. Fine-grained freezing ablations show a marked forgetting drop once frozen parameters exceed roughly 95%, with classifier-only and shallow-adapter baselines approaching LoRA. Companion task-similarity probes in GPT-2 and RoBERTa show the same directional story: frozen-backbone regimes preserve higher inter-task similarity than full fine-tuning, gradual unfreezing weakens stability, and full fine-tuning exhibits its clearest divergence at the final transformer layer. These results support a restrained mechanistic interpretation: LoRA helps largely because backbone freezing preserves a more stable shared feature scaffold. We position standard LoRA as both a strong empirical baseline for sequential encoder adaptation and a useful probe of how selective plasticity shapes interference in transformer continual learning.

Parameter-efficient fine-tuning (PEFT) offers many parameterizations, yet their methodological and functional differences remain unclear. We compare six methods in language and diffusion models to examine how their parameterizations relate to task performance, forgetting, and changes in pretrained weight geometry. Motivated by the spectrum-preserving design of orthogonal fine-tuning (OFT), we first ask whether spectral preservation is itself important for adaptation and retention. We find that the selected LoRA-family methods also approximately preserve pretrained geometry, and that restoring their slightly drifted singular-value spectra largely preserves task performance, questioning the necessity of explicit geometric preservation. Beyond this, we observe that some methods exhibit distinct adaptation--retention trade-offs that vary across settings: LoRA most consistently limits forgetting at competitive performance, DoRA achieves higher mean task scores than LoRA in most comparisons, while PiSSA often incurs greater retention costs. Further intervention experiments suggest that while performance gains from different PEFT methods can be attributed to modifications in different groups of spectral components, we consistently find that restoring dominant rather than intermediate or trailing components produces the largest mean reduction in general-text NLL or base-image drift. Together, these results motivate evaluating geometric constraints through their functional consequences rather than preservation alone. Code is available at https://github.com/Kuaaannn/PEFT_methods.